Geometrie & Funktionen · Common Core Grade 7-8 Geometry (Cylinder Volume), Cambridge IGCSE Physics (Density & Displacement Method), High School Physics (Fluid Statics).
Wasserverdrängungs- & Tauch-Visualisierer
Volumenbestimmung unregelmäßiger Festkörper durch Wasserverdrängung: Überlaufgefäß
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Geometrie-Demofenster● 60 FPS
Experimentelle Steuerungsparameter
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cm
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cm
Echtzeit-Herleitung & Kennzahlen
Aktueller Wasserstand h
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Real-time water depth in bucket
Wasserstandsanstieg Δh
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Height rise above initial h0
Eingetauchte Stablänge
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Wetted length of the rod
Verdrängtes Volumen
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Displaced water volume
Echtzeit-Formelherleitung
Grundformel:
--Einsetzungsschritte:
--Ergebnis: --
Grundschulversion:🎮 Quadernetz, Oberfläche und Volumen ↗
Typische Beispielaufgaben & Prüfungsfallen
Annular Area Contraction: 100 cm² Bucket & 20 cm² Vertical Rod
Aufgabe: A cylindrical bucket with base area 100 cm² contains water to a depth of 16 cm. A sufficiently long iron rod with cross-sectional area 20 cm² is vertically inserted until touching the bottom. What is the new water height?
Analysestrategie: Water volume is invariant: V = 100 × 16 = 1600 cm³. With the rod touching bottom and protruding, water is confined to the annular region with effective base area S_annular = 100 - 20 = 80 cm². New water height h = 1600 / 80 = 20 cm.
Schrittweise Herleitung:
- Step 1: Compute invariant water volume V = 100 × 16 = 1600 cm³.
- Step 2: Effective annular surface area S_eff = 100 - 20 = 80 cm².
- Step 3: New liquid height h = 1600 / 80 = 20 cm.
- Step 4: Water level increase Δh = 20 - 16 = 4 cm.
- Step 5: Verify submerged rod length equals 20 cm (consistent with protruding rod condition).
⚠️ Häufige Fehlvorstellung: Naive non-feedback error: calculating displacement as S_rod × h0 and dividing by S_bucket. The rising water wets additional rod length, which must be solved via effective annular area.
Arbeitsblatt für den Unterricht & Hausaufgaben
Q1. A submerged iron block in a cylinder of radius 10 cm causes water level to rise 3 cm. Find iron volume (π=3.14).
Answer Key: 942 cm³ (3.14 × 10² × 3)
Q2. A rod is pushed down further by 2 cm into a bucket. How does the water level change?
Answer Key: Rises by exactly (2 × S_rod) / (S_bucket - S_rod)
Häufige Fragen & typische Missverständnisse
If the rod is pushed so deep that it becomes fully submerged, does water level keep rising at the accelerated rate?
No! Once the rod tip is fully submerged, displaced volume caps out at the rod's total volume. Pushing it deeper causes no further water level rise.